On the local existence of solutions to the Navier-Stokes-wave system with a free interface

TL;DR

This paper proves the local existence and uniqueness of strong solutions for a coupled Navier-Stokes and elastic body system with free interface in three dimensions, under specific initial regularity conditions.

Contribution

It establishes the first local well-posedness result for the Navier-Stokes-wave system with a free interface in 3D, considering initial data with fractional Sobolev regularity.

Findings

Existence and uniqueness of strong solutions under initial regularity conditions.

Solutions exist locally in time for the coupled fluid-structure system.

The regularity conditions on initial data are optimal for the methods used.

Abstract

We address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space $H^{2+\epsilon}$ and the initial structure velocity is in $H^{1.5+\epsilon}$ , where $\epsilon \in (0, 1/2)$.